Question

Two long, straight wires both carry current to the right, are parallel, and are 25 cm apart. Wire one carries a current of 2.0 A and wire two carries a current of 5.0 A. How far from wire 1 is the net magnetic field equal to 0?

Answer 1

Answer:

x = 7.14 meters

Explanation:

It is given that,

Current in wire 1, $I_1=2\ A$

Current in wire 2, $I_2=5\ A$  

Distance between parallel wires, r = 25 cm

Let at P point the net magnetic field equal to 0. The magnetic field at a point midway between the is given by :

$B=\dfrac{\mu_oI}{2\pi r}$

Let the distance is x from wire 1. So,

$\dfrac{I_1}{r}=\dfrac{I_2}{(0.25-r)}$

$\dfrac{2}{r}=\dfrac{5}{(25-r)}$

$x=\dfrac{50}{7}\ m$

x = 7.14 meters

So, the magnetic field will be 0 at a distance of 7.14 meters from wire 1. Hence, this is the required solution.